In recent years, there have been proposed and developed various adaptive cruise control (ACC) technologies. One such ACC technology has been disclosed in Japanese Patent Provisional Publication No. 2006-321354 (hereinafter is referred to as “JP2006-321354”). The adaptive cruise traveling control system disclosed in JP2006-321354 is configured to execute three different traveling control functions, that is, (i) a first traveling control function (i.e., a cruise control function, namely, cruise-set-speed control at a set vehicle speed set by the driver), (ii) a second traveling control function (i.e., a so-called “following control” that a host vehicle follows a preceding vehicle, while keeping the host vehicle's distance from the preceding vehicle at an approximately constant vehicle-to-vehicle distance, and (iii) a third traveling control function that adjusts the host vehicle speed to an appropriate speed based on road information (in particular, limited vehicle speed information) from a navigation device). When a set vehicle speed exceeds a limited vehicle speed, the adaptive cruise traveling control system disclosed in JP2006-321354 informs the driver about “overspeed” (the set vehicle speed exceeding the limited vehicle speed). If the driver does not change the set vehicle speed for a predetermined elapsed time, measured from the point of time when the “overspeed” information has been outputted to the driver, then the adaptive cruise traveling control system automatically changes the set vehicle speed to the limited vehicle speed, without driver intervention.